diff --git a/NEWS b/NEWS
index 72ff8e454..eadd144ea 100644
--- a/NEWS
+++ b/NEWS
@@ -100,8 +100,16 @@ New in spot 2.8.7.dev (not yet released)
     same transition structure (where the ..._maybe() variant would
     modify the Rabin automaton if needed).
 
-  - to_parity() now combines several strategies for paritizing any
-    automaton.
+  - to_parity() has been rewritten now combines several strategies for
+    paritizing automata with any acceptance condition.
+
+  Backward-incompatible changes:
+
+  - iar() and iar_maybe() have been moved from
+    spot/twaalgos/rabin2parity.hh spot/twaalgos/toparity.hh and marked
+    as deprecated, they should be replaced by to_parity().  In case
+    the input is Rabin-like or Streett-like, to_parity() should be at
+    least as good as iar().
 
 New in spot 2.8.7 (2020-03-13)
 
diff --git a/spot/twaalgos/toparity.cc b/spot/twaalgos/toparity.cc
index 64b9d392e..81118f18b 100644
--- a/spot/twaalgos/toparity.cc
+++ b/spot/twaalgos/toparity.cc
@@ -39,8 +39,8 @@
 namespace spot
 {
 
-// Old version of IAR.
-namespace
+  // Old version of IAR.
+  namespace
   {
 
     using perm_t = std::vector<unsigned>;
@@ -346,31 +346,39 @@ namespace
       std::vector<unsigned> state2pos_iar_states;
       std::vector<std::pair<iar_state, unsigned>> iar_states;
     };
-  }
 
-  twa_graph_ptr
-  iar_maybe_old(const const_twa_graph_ptr& aut, bool pretty_print)
-  {
-    std::vector<acc_cond::rs_pair> pairs;
-    if (!aut->acc().is_rabin_like(pairs))
-      if (!aut->acc().is_streett_like(pairs))
-        return nullptr;
+    // Make this a function different from iar_maybe(), so that
+    // iar() does not have to call a deprecated function.
+    static twa_graph_ptr
+    iar_maybe_(const const_twa_graph_ptr& aut, bool pretty_print)
+    {
+      std::vector<acc_cond::rs_pair> pairs;
+      if (!aut->acc().is_rabin_like(pairs))
+        if (!aut->acc().is_streett_like(pairs))
+          return nullptr;
+        else
+          {
+            iar_generator<false> gen(aut, pairs, pretty_print);
+            return gen.run();
+          }
       else
         {
-          iar_generator<false> gen(aut, pairs, pretty_print);
+          iar_generator<true> gen(aut, pairs, pretty_print);
           return gen.run();
         }
-    else
-      {
-        iar_generator<true> gen(aut, pairs, pretty_print);
-        return gen.run();
-      }
+    }
   }
 
   twa_graph_ptr
-  iar_old(const const_twa_graph_ptr& aut, bool pretty_print)
+  iar_maybe(const const_twa_graph_ptr& aut, bool pretty_print)
   {
-    if (auto res = iar_maybe_old(aut, pretty_print))
+    return iar_maybe_(aut, pretty_print);
+  }
+
+  twa_graph_ptr
+  iar(const const_twa_graph_ptr& aut, bool pretty_print)
+  {
+    if (auto res = iar_maybe_(aut, pretty_print))
       return res;
     throw std::runtime_error("iar() expects Rabin-like or Streett-like input");
   }
diff --git a/spot/twaalgos/toparity.hh b/spot/twaalgos/toparity.hh
index c9c45bd00..0b806d6c1 100644
--- a/spot/twaalgos/toparity.hh
+++ b/spot/twaalgos/toparity.hh
@@ -91,7 +91,7 @@ namespace spot
   /// It is better to use to_parity() instead, as it will use better
   /// strategies when possible, and has additional optimizations.
   SPOT_API twa_graph_ptr
-  to_parity_old(const const_twa_graph_ptr& aut, bool pretty_print=false);
+  to_parity_old(const const_twa_graph_ptr& aut, bool pretty_print = false);
 
   /// \ingroup twa_acc_transform
   /// \brief Turn a Rabin-like or Streett-like automaton into a parity automaton
@@ -113,17 +113,18 @@ namespace spot
   ///
   /// It is better to use to_parity() instead, as it will use better
   /// strategies when possible, and has additional optimizations.
+  SPOT_DEPRECATED("use to_parity() instead") // deprecated since Spot 2.9
   SPOT_API twa_graph_ptr
-  iar_old(const const_twa_graph_ptr& aut, bool pretty_print = false);
+  iar(const const_twa_graph_ptr& aut, bool pretty_print = false);
 
   /// \ingroup twa_acc_transform
   /// \brief Turn a Rabin-like or Streett-like automaton into a parity automaton
   /// based on the index appearence record (IAR)
   ///
   /// Returns nullptr if the input automaton is neither Rabin-like nor
-  /// Streett-like, and calls spot::iar_old() otherwise.
-  SPOT_API
-  twa_graph_ptr
-  iar_maybe_old(const const_twa_graph_ptr& aut, bool pretty_print = false);
+  /// Streett-like, and calls spot::iar() otherwise.
+  SPOT_DEPRECATED("use to_parity() and spot::acc_cond::is_rabin_like() instead")
+  SPOT_API twa_graph_ptr   // deprecated since Spot 2.9
+  iar_maybe(const const_twa_graph_ptr& aut, bool pretty_print = false);
 
 } // namespace spot
diff --git a/tests/python/except.py b/tests/python/except.py
index fbcc1563e..926aa864d 100644
--- a/tests/python/except.py
+++ b/tests/python/except.py
@@ -33,7 +33,7 @@ def report_missing_exception():
 aut = spot.translate('GFa & GFb & GFc')
 aut.set_acceptance(spot.acc_cond("parity min even 4"))
 try:
-    spot.iar_old(aut)
+    spot.iar(aut)
 except RuntimeError as e:
     assert 'iar() expects Rabin-like or Streett-like input' in str(e)
 else: